It looks like you're focussing too much on doing the hard plumbing with jQuery yourself. The reason for the error appears to be that -obviously- Materialize js isn't properly loaded. Without knowing the specifics on the bundler or startup project type you're using, and how it's setup, this is hard to give an answer to.
However, what might benefit you is that there is an officially supported project called the Aurelia Materialize Bridge, which is an Aurelia-specific wrapper for the Materialize.css library.
To get started:
- Remove everything you've manually added, regarding the materialize lib
- Walk through the installation instructions
- Finally, have a look at the samples to see how you get things started
In your example, setting up the basic slider is as easy as for example:
<template>
<md-slider>
<li>
<img src="http://lorempixel.com/580/250/nature/1" />
<div class="caption center-align">
<h3>This is our big Tagline!</h3>
<h5 class="light grey-text text-lighten-3">Here's our small slogan.</h5>
</div>
</li>
<li>
<img src="http://lorempixel.com/580/250/nature/2" />
<div class="caption left-align">
<h3>Left Aligned Caption</h3>
<h5 class="light grey-text text-lighten-3">Here's our small slogan.</h5>
</div>
</li>
<li>
<img src="http://lorempixel.com/580/250/nature/3" />
<div class="caption right-align">
<h3>Right Aligned Caption</h3>
<h5 class="light grey-text text-lighten-3">Here's our small slogan.</h5>
</div>
</li>
<li>
<img src="http://lorempixel.com/580/250/nature/4" />
<div class="caption center-align">
<h3>This is our big Tagline!</h3>
<h5 class="light grey-text text-lighten-3">Here's our small slogan.</h5>
</div>
</li>
</md-slider>
</template>
As a rule of thumb; you shouldn't have to use any jQuery-like syntax at all.
Hope this helps you out.